To illustrate the relationship between a freely falling object's gravitational potential energy (\(PE\)) and its height (\(h\)) from the ground, you can create a graph that plots gravitational potential energy on the y-axis and height on the x-axis.
Graph Details:
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Y-Axis: Gravitational Potential Energy (PE), measured in joules (J). The formula for gravitational potential energy is: \[ PE = mgh \] where:
- \(m\) is the mass of the object (in kg),
- \(g\) is the acceleration due to gravity (approximately 9.81 m/s² on Earth),
- \(h\) is the height (in meters).
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X-Axis: Height (h), measured in meters (m).
Relationship:
- The gravitational potential energy is directly proportional to the height of the object.
- As the height increases, the gravitational potential energy also increases linearly.
- The line will start from the origin (0,0) where there is no height and thus no potential energy, and it will slope upward as height increases.
Example:
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If the mass of the object is 1 kg:
- At height \(h = 0\): \(PE = 1 \times 9.81 \times 0 = 0\) J
- At height \(h = 1\): \(PE = 1 \times 9.81 \times 1 = 9.81\) J
- At height \(h = 2\): \(PE = 1 \times 9.81 \times 2 = 19.62\) J
- At height \(h = 3\): \(PE = 1 \times 9.81 \times 3 = 29.43\) J
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End Points to Plot:
- (0, 0),
- (1, 9.81),
- (2, 19.62),
- (3, 29.43), ... etc.
Graph Representation:
You can visualize it as a straight line starting from the origin (0,0) and extending upward to the right. The gradient of the line indicates the acceleration due to gravity, which remains constant.
If you want to create this graph using graphing software or tools, you can input these values to generate a straight line.